The intensity of sound is x W/m2 at a distance of 5 m from the source. What is the intensity of the sound at a distance of 20 m from the source?
I am not sure how to do this problem. Thank you for your help!
I = (5^2/20^2)*X = (1/16)X W/m^2.
To find the intensity of sound at a distance of 20 m from the source, we can use the inverse square law. According to the inverse square law, the intensity of sound decreases as the square of the distance from the source increases.
The formula for the inverse square law is:
I2 = I1 × (D1/D2)^2
Where:
I1 is the initial intensity of sound at distance D1
I2 is the intensity of sound at distance D2
In this case, we are given that the intensity of sound at a distance of 5 m from the source is x W/m^2. We want to find the intensity of sound at a distance of 20 m from the source.
So we plug the given values into the formula:
I2 = x × (5/20)^2
Simplifying this expression gives us:
I2 = x × (1/4)^2
= x × 1/16
= x/16
Therefore, the intensity of sound at a distance of 20 m from the source would be x/16 W/m^2.
To find the intensity of sound at a distance of 20 m from the source, we can use the inverse square law for sound propagation. According to this law, the intensity of sound is inversely proportional to the square of the distance from the source.
Mathematically, this can be written as:
I1 / I2 = (d2 / d1)^2
where:
I1 is the initial intensity of sound at distance d1,
I2 is the final intensity of sound at distance d2,
and ^2 denotes squaring.
In this case, we are given that the intensity of sound is x W/m^2 at a distance of 5 m from the source.
Let's substitute the given values into the formula and solve for I2:
I1 / I2 = (d2 / d1)^2
x / I2 = (20 / 5)^2
x / I2 = 16
To isolate I2 (the final intensity), we can rearrange the equation:
I2 = x / 16
Therefore, the intensity of sound at a distance of 20 m from the source is x/16 W/m^2.
Remember, the inverse square law can be applied to various physical phenomena where the intensity diminishes with distance, such as light, gravity, and electric fields.